相关论文: Making Birth-Death Processes from Backward Fokker-…

Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic…

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…

We study two time-changed variants of the birth-death process with catastrophe where the time-changing components are the first hitting times of the stable subordinator and the tempered stable subordinator. For both the processes, we derive…

A new stochastic method for describing mortality is proposed and explored. It is based on differences of observed times series of the transform $\log(-\log x)$ of survival probabilities which seem to follow simple patterns over the years.…

We propose a new approach to constructing a neural network for predicting expectations of stochastic differential equations. The proposed method does not need data sets of inputs and outputs; instead, the information obtained from the…

Recently, a novel framework to handle stochastic processes has emerged from a series of studies in biology, showing situations beyond 'It\^o versus Stratonovich'. Its internal consistency can be demonstrated via the zero mass limit of a…

A method yielding simple relationships among bilateral birth-and-death processes is outlined. This allows one to relate birth and death rates of two processes in such a way that their transition probabilities, first-passage-time densities…

By decoupling forward and backward stochastic trajectories, we construct a family of martingales and work theorems for both overdamped and underdamped Langevin dynamics. Our results are made possible by an alternative derivation of work…

The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to…

We develop a stochastic calculus for processes which are built by convoluting a pure jump, zero expectation L\'{e}vy process with a Volterra-type kernel. This class of processes contains, for example, fractional L\'{e}vy processes as…

This paper is concerned with a class of multivariable stochastic Hamiltonian systems whose generalised position is related by an ordinary differential equation to the momentum governed by an Ito stochastic differential equation. The latter…

We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter…

Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme…

Given a discrete stochastic process, for example a chemical reaction system or a birth and death process, we often want to find a continuous stochastic approximation so that the techniques of stochastic differential equations may be brought…

In this paper we explore the life expectancy limits by based on the stochastic modeling of mortality and applying the first exit or hitting time theory of a stochastic process. The main assumption is that the health state or the "vitality",…

Birth-death processes (BDPs) are continuous-time Markov chains that track the number of "particles" in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle…

We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the…

We use methods from combinatorics and algebraic statistics to study analogues of birth-and-death processes that have as their state space a finite subset of the $m$-dimensional lattice and for which the $m$ matrices that record the…

Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite dimensional) Wiener…

Spatially dependent birth-death processes can be modelled by kinetic models such as the BBGKY hierarchy. Diffusion in infinite dimensional systems can be modelled with Brownian motion in Hilbert space. In this work Doi field theoretic…